A First Course in Linear Algebra
A First Course in Linear Algebra (UNSW). Taught by Professor N. J. Wildberger, this course presents a geometrical view to Linear Algebra, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine geometry, which is the natural setting for vectors. Flexibility in choosing coordinate frameworks is important for understanding the subject. Determinants also play a key role, and these are introduced in the context of multi-vectors in the sense of Grassmann. The course features a careful treatment of polynomial spaces, with applications to Stirling numbers and cubic splines.
| Lecture 15 - Applications of Row Reduction (Gaussian Elimination) I |
This lecture shows how the three main problems of Linear Algebra can be tackled using the algorithm of row reduction, also called Gaussian elimination. The three main problems are: how to invert a linear change of coordinates, how to compute the eigenvalues and eigenvectors of a square matrix, and how to compute the determinant of a square matrix.
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